Answer:
σ² = 82.556; σ = 9.086
Step-by-step explanation:
It would be easy to do this in a statistical calculator. but I suspect they want you to do it by hand.
It helps to arrange your calculations in the form of a table.
[tex]\begin{array}{rrr}\mathbf{x} & \mathbf{x - \mu} & \mathbf{(x - \mu)^{2}}\\14 & -0.667 &0.44\\5 & -9.667 & 93.44\\12 & -2.667 & 7.11\\4 & -10.667 & 113.78\\26 & 11.333 & 128.46\\27 & 12.333 & 152.11\\\sum = \mathbf{88} & & \mathbf{495.33}\\\end{array}\\[/tex]
1. Calculate the mean (µ)
(a) Count the elements in the data set
n = 6
(b) Calculate the sum of the terms
[tex]\displaystyle \text{Sum} = \sum_{i = 1}^{6}x_{i} = 88[/tex]
(c) Divide the sum by the number of terms
[tex]\mu = \dfrac{1}{6} \times 88 = 14.667[/tex]
2. Calculate the variance
(a) Subtract the mean from each data point
(b) Square the differences
(c) Add the squares
[tex]\displaystyle \text{Sum} = \sum_{i = 1}^{6}(x_{i} - \mu)^{2} = 495.33[/tex]
(d) Divide the sum by the number of terms
[tex]\displaystyle \text{Variance} = \sigma^{2} = \frac{1}{6 }\sum_{i = 1}^{6}(x_{i} - \mu)^{2} = \mathbf{82.556}[/tex]
3. Calculate the standard deviation
The standard deviation is the square root of the variance.
[tex]\sigma = \sqrt{82.556} = \mathbf{9.086}[/tex]
